This paper presents a general-equilibrium model of endogenous skilled-biased technological change and matching unemployment in a disaggregated economy. We simultaneously endogenise both the direction and pace of technological change as well as the unemployment rates. We show that an increase in the supply of high-skilled labour can explain skilled-biased technological change, a reduction in high-skilled unemployment and a rise in the high-skilled wage differential. In accordance with convincing empirical evidence, the high-skilled suffer from shorter and fewer spells of unemployment.